# Prime Factorization Calculator

The prime factorization calculator will take any numbers and find its prime factors. To understand the whole process, first you must understand the concept of a prime number. A prime number is any number whose only factors are one and itself. A key point to note is that there must be two different factors, so 1 is not a prime number, since both factors of 1 are the same. For example, 5 is a prime number since the only factors of 5 are 1 and 5. Moving a step further to understand this process, we must answer, "what is a prime factor?" and "what is prime factorization?"

## What is a Prime Factor?

Prime factors are factors of a number that themselves are prime numbers. For example, suppose we want to get the factors of 20. That is, we want to know what whole numbers multiply to give you 20. We know that `1 * 20 = 20`

, `2 * 10 = 20`

and `4 * 5 = 20`

. But notice that `20, 10`

and `4`

are not prime factors. The only prime factors of `20`

are `2`

and `5`

. You can also get these factors with the use of our factor calculator.

## What is Prime Factorization?

Prime factorization is when we break a number down into factors that are only prime numbers. If we look at the above example with 20, the factors are `1, 2, 4, 5, 10, 20`

. The best playce to start is to find at least one initial factor that is prime. Since 5 is prime, we can start with `4 * 5`

. Notice that 4 is not prime, so we break 4 down into `2 * 2`

. Since 2 is primse, the primae factorization of 20 is `2 * 2 * 5`

. Go and check this result with our prime factorization calculator.

## Greatest Common Factor

The use of the prime factorization calculator is also useful in finding the greatest common factor. The greatest common factor is important when adding fractions with unlike denominators. The greateset common factor is obtained when multiplying the higher powers of all factors between the two numbers. For exampole, the greatest common factor between 6 and 20 is `(2 * 2 * 3 * 5) = 60`

. Thie can be obtained by hand or with use of the greatest common factor calculator Notice the list of prime factoizations below, which can be checked using our prime factorization calculator.

- Prime factorization of 2: it's a prime number!
- Prime factorization of 3: it's a prime number!
- Prime factorization of 4: 2 * 2
- Prime factorization of 5: it's a prime number!
- Prime factorization of 6: 2 * 3
- Prime factorization of 7: it's a prime number!
- Prime factorization of 8: 2 * 2 * 2
- Prime factorization of 9: 3 * 3
- Prime factorization of 10: 2 * 5
- Prime factorization of 11: it's a prime number!
- Prime factorization of 12: 2 * 2 * 3
- Prime factorization of 13: it's a prime number!
- Prime factorization of 14: 2 * 7
- Prime factorization of 15: 3 * 5
- Prime factorization of 16: 2 * 2 * 2 * 2
- Prime factorization of 17: it's a prime number!
- Prime factorization of 18: 2 * 3 * 3
- Prime factorization of 19: it's a prime number!
- Prime factorization of 20: 2 * 2 * 5
- Prime factorization of 21: 3 * 7
- Prime factorization of 22: 2 * 11
- Prime factorization of 23: it's a prime number!
- Prime factorization of 24: 2 * 2 * 2 * 3
- Prime factorization of 25: 5 * 5
- Prime factorization of 26: 2 * 13
- Prime factorization of 27: 3 * 3 * 3
- Prime factorization of 28: 2 * 2 * 7
- Prime factorization of 29: it's a prime number!
- Prime factorization of 30: 2 * 3 * 5
- Prime factorization of 31: it's a prime number!
- Prime factorization of 32: 2 * 2 * 2 * 2 * 2
- Prime factorization of 33: 3 * 11
- Prime factorization of 34: 2 * 17
- Prime factorization of 35: 5 * 7
- Prime factorization of 36: 2 * 2 * 3 * 3
- Prime factorization of 37: it's a prime number!
- Prime factorization of 38: 2 * 19
- Prime factorization of 39: 3 * 13
- Prime factorization of 40: 2 * 2 * 2 * 5
- Prime factorization of 41: it's a prime number!
- Prime factorization of 42: 2 * 3 * 7
- Prime factorization of 43: it's a prime number!
- Prime factorization of 44: 2 * 2 * 11
- Prime factorization of 45: 3 * 3 * 5
- Prime factorization of 46: 2 * 23
- Prime factorization of 47: it's a prime number!
- Prime factorization of 48: 2 * 2 * 2 * 2 * 3
- Prime factorization of 49: 7 * 7
- Prime factorization of 50: 2 * 5 * 5
- Prime factorization of 51: 3 * 17
- Prime factorization of 52: 2 * 2 * 13
- Prime factorization of 53: it's a prime number!
- Prime factorization of 54: 2 * 3 * 3 * 3
- Prime factorization of 55: 5 * 11
- Prime factorization of 56: 2 * 2 * 2 * 7
- Prime factorization of 57: 3 * 19
- Prime factorization of 58: 2 * 29
- Prime factorization of 59: it's a prime number!
- Prime factorization of 60: 2 * 2 * 3 * 5
- Prime factorization of 61: it's a prime number!
- Prime factorization of 62: 2 * 31
- Prime factorization of 63: 3 * 3 * 7
- Prime factorization of 64: 2 * 2 * 2 * 2 * 2 * 2
- Prime factorization of 65: 5 * 13
- Prime factorization of 66: 2 * 3 * 11
- Prime factorization of 67: it's a prime number!
- Prime factorization of 68: 2 * 2 * 17
- Prime factorization of 69: 3 * 23
- Prime factorization of 70: 2 * 5 * 7
- Prime factorization of 71: it's a prime number!
- Prime factorization of 72: 2 * 2 * 2 * 3 * 3
- Prime factorization of 73: it's a prime number!
- Prime factorization of 74: 2 * 37
- Prime factorization of 75: 3 * 5 * 5
- Prime factorization of 76: 2 * 2 * 19
- Prime factorization of 77: 7 * 11
- Prime factorization of 78: 2 * 3 * 13
- Prime factorization of 79: it's a prime number!
- Prime factorization of 80: 2 * 2 * 2 * 2 * 5
- Prime factorization of 81: 3 * 3 * 3 * 3
- Prime factorization of 82: 2 * 41
- Prime factorization of 83: it's a prime number!
- Prime factorization of 84: 2 * 2 * 3 * 7
- Prime factorization of 85: 5 * 17
- Prime factorization of 86: 2 * 43
- Prime factorization of 87: 3 * 29
- Prime factorization of 88: 2 * 2 * 2 * 11
- Prime factorization of 89: it's a prime number!
- Prime factorization of 90: 2 * 3 * 3 * 5
- Prime factorization of 91: 7 * 13
- Prime factorization of 92: 2 * 2 * 23
- Prime factorization of 93: 3 * 31
- Prime factorization of 94: 2 * 47
- Prime factorization of 95: 5 * 19
- Prime factorization of 96: 2 * 2 * 2 * 2 * 2 * 3
- Prime factorization of 97: it's a prime number!
- Prime factorization of 98: 2 * 7 * 7
- Prime factorization of 99: 3 * 3 * 11
- Prime factorization of 100: 2 * 2 * 5 * 5